I think I have a couple of suggestions:
Find a current social/scientific norm that maps almost perfectly to Archimedes’ time that you disagree with (e.g. the need for a strong, expansionist military; use of torture; increase in state power over citizens; existence of a political class etc.) and use the same arguments against it now, including outcomes and dangers, and they should map to decent arguments then.
Find a socially wronged group and use arguments for their emancipation (women, non-whites, gays, children etc. depending on your era) and whichever hated/discriminated against group they map to in Archimedes’ time will almost definitely be helped by your emancipation arguments.
Say that hatred/fear based on religion is wrong, but that religion itself is wrong and the acquiescence to authority is also problematic.
Describe the problems of current economic bubbles, their causes and possible solutions to avoid them. This will hopefully help with the basic economy of ancient Greece.
Argue for non-objective morality. And moral error theory. And a lack of libertarian free will. And against fate (but for a QM-accepting variant of determinism).
Basically, as long as your argument is against the common knowledge/understanding of your time you have a chance of getting across a decent version of it, or the principle at least, especially if the common knowledge has a (close) corollary in Archimedes’ time. (HT. unequally-yoked).
Ahh, but, you see, it’s their choice to go to hell and not something the omni-benevolent creator of the universe does. But obviously it’s their choice at the instant of death and not a moment afterwards when they realise that god actually exists, one can’t repent or believe then...
Blame The Victim #Christianity